DRY 9: Drying Kinetics and Equilibria
     Part 1: Introduction
         1. STATEMENT OF PURPOSE
             1.1 Why this Report Exists
             1.2 Aims of the Volume
         2. HOW TO USE THIS MANUAL VOLUME
             2.1 Theoretical aspects
             2.2 Practical aspects
     Part 2: Theory (State of the Science)
         1. INTRODUCTION
             1.1 Purpose and Contents
         2. LITERATURE BACKGROUND
             2.1 Historical review
             2.2 Nature of moist materials
             2.3 Kinetics
         3. BASIC CONCEPTS
             3.1 Definitions
             3.2 Simple drying theory
             3.3 Convection drying
                 3.3.1 Induction period
                 3.3.2 Constant rate or unhindered drying period
                 3.3.3 Falling rate or hindered drying period
                 3.3.4 Practical drying curves
             3.4 Contact drying
             3.5 Drying in pure vapour
                 3.5.1 General principles
                 3.5.2 Drying in superheated steam
                 3.5.3 Vacuum drying and nitrogen bleeds
             3.6 Dielectric drying
             3.7 Drying with reaction
         4. MOISTURE EQUILIBRIUM
             4.1 Definition
             4.2 Mechanisms of moisture sorption
             4.3 Empirical relationships and correlations
             4.4 Heat of wetting
             4.5 Response to environmental changes
             4.6 Drying of solvates
         5. TRANSPORT PROCESSES IN SOLIDS
             5.1 Moisture movement in solids
             5.2 Driving force for moisture movement
             5.3 Internal heat transfer
             5.4 External heat transfer
                 5.4.1 Introduction
                 5.4.2 Dispersion dryers
                 5.4.3 Through-circulation dryers
                 5.4.4 Cross-circulation dryers
         6. CONSTRUCTING A DRYING MODEL BASED ON PHYSICS
             6.1 Review of existing models
                 6.1.1 Diffusion (Fickian) models
                 6.1.2 Receding evaporative front models
                 6.1.3 Wetted surface models
                 6.1.4 Capillary model
                 6.1.5 Surface diffusion model
                 6.1.6 General theories of drying
             6.2 Continuum mechanics
             6.3 A rigorous model
         7. GENERAL THEORIES OF DRYING
             7.1 Irreversible Thermodynamics
             7.2 Krischer's Method
             7.3 Volume-averaging methods
         8. DRYING KINETICS MODELS BASED ON SIMPLIFIED PHYSICS
             8.1 Definition
             8.2 Superficial Drying
             8.3 Wetted-surface control
             8.4 Receding evaporative front
             8.5 Diffusional models
         9. SIMPLIFIED SCALING METHODS
             9.1 Thijssen and Coumans' method
             9.2 The characteristic drying curve (Van Meel's method)
         10. COMPARISON OF THE DIFFERENT MODELS
             10.1 Requirements for practical application
             10.2 Methodology
             10.3 Drying above the boiling point
                 10.3.1 Reference case and fitting of the parameters
                 10.3.2 Response to changes in external conditions
             10.4 Drying below the boiling point
                 10.4.1 Reference case and fitting of the model parameters
                 10.4.2 Response to changed conditions
             10.5 External conditions varying with time
                 10.5.1 Drying above the boiling point
                 10.5.2 Drying below the boiling point
             10.6 Diffusion coefficient
             10.7 Simulation of other materials
             10.8 Comparison of the models with experimental data
                 10.8.1 Reference case
                 10.8.2 Response to changes in drying conditions
             10.9 Discussion and conclusions
         11. DRYING IN LAYERS
             11.1 Deviations from ideal behaviour
             11.2 Humidity variations through a layer
             11.3 Number of transfer units (NTU) concept
             11.4 Drying rate variation through a layer
             11.5 Humidity potential
             11.6 Critical moisture content
             11.7 Application to dryers
             11.8 Application to drying kinetics
             11.9 Mathematical analysis
             11.10 Simplified analysis of convective layer drying (no agitation)
         12. BATCH DRYING
             12.1 Introduction
             12.2 Convective Batch Drying without Air Recycle
             12.3 Convective Batch Drying With Recycle
             12.4 Contact Heat Transfer to Particles
             12.5 Conclusions
         13. SELECTIVE DRYING
             13.1 Definition
             13.2 Evaporation of binary mixtures
             13.3 Evaporation of secondary solvents
         14. REFERENCES
         15. NOMENCLATURE
         16. APPENDIX. HUMIDITY TERMINOLOGY, DEFINITIONS AND SYMBOLS
     Part 3: Applications
         1. INTRODUCTION
         2. PRINCIPLES OF DRYING KINETICS MEASUREMENT
             2.1 Introduction
             2.2 Methods of measuring moisture loss
             2.3 Methods based on recording fundamental drying kinetics
                 2.3.1 Single particle kinetics measurements
                 2.3.2 Multiple particle kinetics
                 2.3.3 Thin layer drying method
             2.4 Methods based on small-scale equivalents to the dryer
                 2.4.1 Deep bed or tray drying
                 2.4.2 Fluidised bed drying
             2.5 Practical bench scale test methods
             2.6 Direct (in Situ) Weighing
                 2.6.1 Particles
                 2.6.2 Liquid and slurry droplets
             2.7 Moisture-Loss (Humidity) Monitoring
                 2.7.1 Note on humidity terminology
             2.8 Conclusions
         3. MANIPULATION OF EXPERIMENTAL DATA
             3.1 Objective
             3.2 Methodology
                 3.2.1 Interconversion of curves
                 3.2.2 Assessment of the Data
                 3.2.3 Determination from Weight-Loss Data
                 3.2.4 Determination from Humidity Data
                 3.2.5 Fitting and smoothing batch drying curves
             3.3 Interpretation of drying curves
             3.4 Obtaining and processing the characteristic drying curve
                 3.4.1 Derivation and fitting equations
                 3.4.2 Correcting the characteristic curve for bed effects
                 3.4.3 Effective use of the characteristic curve
             3.5 Using the characteristic drying curve for design
                 3.5.1 Materials showing an unhindered drying period
                 3.5.2 Materials without an unhindered drying period
                 3.5.3 Worked example
                 3.5.4 Interpolating and extrapolating drying curves
             3.6 Drying coefficient
             3.7 Fluidised Bed Tests
                 3.7.1 Methods for processing data
                 3.7.2 Choice of conditions for fluid bed kinetics testing
             3.8 Practical problems of measurement
                 3.8.1 Low drying rates
                 3.8.2 Hygroscopicity, channelling and bypass effects in kinetics tests
                 3.8.3 The material history problem
             3.9 Using the DRYCUR software
                 3.9.1 Operation
                 3.9.2 Technical Details
                 3.9.3 Kinetics
         4. EQUILIBRIUM MOISTURE CONTENT DETERMINATION
             4.1 Experimental Methods
                 4.1.1 Static method
                 4.1.2 Dynamic method
             4.2 Choice of conditions for equilibrium moisture content testing
             4.3 Use of DRYCUR to process equilibria data
             4.4 Possible future developments
         5. DRYING UNDER COMMERCIAL CONDITIONS
             5.1 Drying under Constant External Conditions
             5.2 Cross-circulation under variable external conditions
             5.3 Through-circulation Drying
             5.4 Well-mixed Solids Arrangements
             5.5 Convective Batch Drying With Recycle
             5.6 Contact Heat Transfer to Particles
             5.7 Drying of layers and batch drying curves
                 5.7.1 Deviations from ideal behaviour
                 5.7.2 Humidity and drying rate variations through a layer
                 5.7.3 Drying rate variation through a layer
                 5.7.4 Application to dryers
                 5.7.5 Application to drying kinetics
         6. PRACTICAL MEASUREMENT METHODS FOR INDUSTRIAL DRYERS
             6.1 Assessment of the characteristic drying curve
             6.2 Pneumatic conveying dryers
                 6.2.1 Suitable methods
                 6.2.2 Data processing and incorporation in the model
                 6.2.3 Typical drying kinetics
             6.3 Spray dryers
                 6.3.1 Suitable methods
                 6.3.2 Data manipulation
                 6.3.3 Typical drying kinetics
                 6.3.4 Approximate calculation method
             6.4 Fluidised bed dryers
                 6.4.1 Suitable methods
                 6.4.2 Scaling and data manipulation
                 6.4.3 Typical drying kinetics
             6.5 Cascading rotary dryers
             6.6 Layer dryers - general
             6.7 Through-circulation dryers
             6.8 Cross-circulated dryers
             6.9 Contact dryers
             6.10 Dielectric dryers
             6.11 Conclusions
         7. REFERENCES
         8. NOMENCLATURE
     Terms and Conditions of Use

• Part 1 Introduction
• Part 2 Theoretical models
• Part 3 Application to industrial dryers

This volume, having undergone extensive revision and expansion from earlier drafts as a result of developments in SPS research, notably through the "QUID" project described in Section 6. Interim drafts have been available throughout and have been presented at various Drying Panel meetings. It considers in depth the "material model", looking at the relationship of drying to moisture movement in particles and assessing how the various drying models may be used in practice.

Volume DRY IX   Part 1 Introduction.

This is a brief introduction outlining the principles and giving the structure.

---

Volume DRY IX   Part 2 Theory.

This part reviews available theories in depth. The section on drying kinetics includes the characteristic drying curve, receding evaporative interface and diffusion models. The rigorous models developed by Whitaker and others, based on continuum mechanics, are discussed and compared with the simpler models above. This section was greatly expanded in 1997 as a result of the knowledge gained through the CEC-funded "QUID" research project, described in Section 6. Other subjects covered include heat of wetting and selective drying. The discussion of drying equilibria is a considerable expansion of the work reported in RR35, making use of more recent experimental results from the SPS equilibrium moisture content rig, correlations suggested by other workers worldwide and insights from adsorption theory.

---

Volume DRY IX   Part 3 Application.

An important difference of this Volume from previous published work on drying kinetics is a strong emphasis on how to apply the principles in real industrial practice. Applications to different types of dryers are explained, showing which types of kinetic models are appropriate for each type and why. The use of the computer program DRYCUR to transform kinetics data into the various forms required by different dryer models is also covered, and methods to record the experimental data in dedicated rigs or bench-scale tests are described.